JOURNAL

OF APPLIED

PHYSIOLOGY Printed

Vol. 26, No. 5, May 1969.

in U.S.A.

Mechanical

components

of human

eye movements

D. A. ROBINSON, D. iM. O’MEARA, A. B. SCOTT, AND C. C. COLLINS Smith-Kettlewell Institute of Visual Sciences, Pacijc Medical Center, San Francisco, California 94LL5; and Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205

ROBINSON, D. A., D. hf. O'MEARA, A. B. SCOTT, AND C. C. COLLINS. Mechanical components of human eye movements. J. Appl. Physiol. 26(5) : 548-553. 1969.~The isometric tensions of three lateral rectus muscles of three patients were measured while detached from the globe during strabismus surgery together with the force required to rotate the globe horizontally with both horizontal recti detached. The length-tension relationship was measured for several levels of innervation by requesting the patient to make known eye movements with the unoperated eye. Muscle tone in the primary position of gaze ranged from 12 to 17 g. The slope of the length-tension curve near the primary position was about 0.45 g/deg. The spring constant of the passive muscle components was about 0.25 and 0.33 g/deg for the globe suspensory tissues. This makes it possible to estimate the division of forces between agonist, antagonist, and suspensory tissues for any angle of gaze. The time course of isometric tension associated with saccades clearly reveals the pulsatile nature of net active state tension that accounts for the rapidity of saccadic e

muscle

mechanics;

extraocular

muscles

created by moving the intact eye is the sum of the forces of the agonist muscle, antagonist, and suspensory tissues whose individual contributions are unknown. When strabismus surgery is performed under topical anesthesia an opportunity arises to measure the mechanical forces of these elements separately, and the results of three such experiments are reported here. The principal goal of the study was to obtain the length-tension relationship of human extraocular muscles at various levels of innervation. The information reported here should also be useful in the diagnosis and correction of extraocular muscle disorders, both peripheral and central. It should permit recognition of abnormalities in quantitative forced duction tests, aid in the design of prosthetic implants, and be of some help in determining the nature and amount of surgical corrections for oculomotor disorders through theoretical considerations or measurements made before or at the time of surgery. METHODS

I

N ORDER TO UNDERSTAND the neural organization of eye movements it is desirable to have a quantitative, analytic description of the relationship between motor nuclei activity and the eye movement it produces. Such studies were begun by Westheimer in 1954 (23) and continued by Vossius (ZZ), Robinson (15, 16), Thomas (21), Childress and Jones (5), and Cook and Stark (6, 7). These descriptions utilized data obtained on the intact human eye, usually the time course of normal saccadic eye movernents but also, in some exthe movements which result from known periments, forces applied through a contact lens. These investigators have proposed models of orbital mechanics which share a broad base of agreement but differ in the quantitative particulars. This is because the available physiological measurements are too few compared to the number of participating mechanical components whose behavior is poorly understood. Consequently many models can fit the available data and more experimental measurements are needed. Part of this indeterminancy is caused by the fact that any reactive force

Through the kind cooperation of the Medical Facility at the Vacaville Prison of the state of California, studies were made with informed consent on the lateral recti of patients in the course of corrective surgery under topical anesthesia for intermittent exotropia. The patients lay supine and a vacuum sandbag pillow was used to reduce head movements. After the medial and lateral recti were detached and prior to their corrective reattachment, the lateral rectus in each case was connected to a strain gauge through a double thickness of 000 surgical silk thread. Isometric muscle tension was recorded on a pen recorder and analogue magnetic tape with a bandwidth of O-625 cycles/set. Three types of measurements were made. To obtain the length-tension relationship of the muscles the patients were asked to make saccadic fixation changes with their normal eye (the operated eye was occluded) from the primary position to target lamps at angles of *15 and &30 deg. The strain gauge was mounted so that the length of the muscle under test could be changed. The muscle was initially adjusted to its normal length

MECHANICAL

COMPONENTS

OF EYE

MOVEMENTS

in the primary position of gaze and then changed by &2, &5, and rt8 mm. At each length the patient scanned the fixation lamp array five times stopping at each target for about 2 sec. Although pulling on the extraocular muscle tendons can cause pain, the extensions used (8 mm) and tensions recorded (up to 110 g) did not, upon inquiry, cause pain to any of the patients. The thread running from muscle to strain gauge lay in a parasagittal plane and was not colinear with the long axis of the muscle. When the muscle developed tension it could slightly press the globe nasally. This would be equivalent to a small compliance added to the strain gauge. It is difficult to estimate this compliance but it must have been quite small ih view of the rapid tension changes recorded. The second procedure was designed to measure the passive length-tension relationship of the muscles. The patient was asked to fixate a lamp held as far out of the field of action of the muscle under study as possible. The tension of the muscle in this relaxed condition was then measured over the same length range. This procedure was repeated on five additional muscles on four patients under general anesthesia. The third procedure measured the force of passive globe rotation with the horizontal recti detached. The strain gauge was attached to the globe (the muscle insertion) by sutures running tangential to the globe and the eye was then abducted in increments up to 4 deg while tension was continuously recorded. These data have been gained from adult patients who were fully aware of this addition to the strabismus procedure which was clinically required. In fact, these kinds of measurements have long been made to help in deciding the amount and kind of strabismus surgery needed. The subjective estimate by the surgeon of the resistance to pulling the eye grasped by a forceps is replaced in these studies by a more refined and quantitative technique. RESULTS

The results arc divided into static and dynamic behavior. The former is divided into the length-tension relationship of the active and passive part of the muscl and of the globe suspensory tissues. For comparison A. Mechanical conpurposes Figs. l-4 relate to patient stants measured for all patients are shown in Table 1. Actiue muscle tension. The isometric tension recorded during 15- and 30-deg saccades into and out of the field of action of the muscle is shown in Fig. 1. After an initial transient the tension approached a constant holding value associated with each position of fixation. The average of the five steady-state tensions recorded at each fixation angle and muscle length constitute a single point in Fig. 2. The solid lines show the relationship between length and tension over an 8-mm range on either side of the primary position length .L, for the effort associated with the deviation of the other eve

549 TABLE

1.

elements

Length-tension

of

human

sjbring eye

constants

of

mechanical

positioning

Patient Age,

sex

&(g);

primary

K, (g/deg)

position

; length

Kpm (g/deg);

length-

Kpo(g/deg);

length-

K,

(g/deg);

total

K,

(g/deg);

chaqge

tone

1 17.01

- developed

tension

possi ve muscle tension spring

tension

slope

of passive

constant

= ,?(K,

in isometric

16.01

12.01

/ 13.7

slope

tension

All values refer to behavior length Lp.

slope orbital

tissues

0.500.20

f Kpm)

f Kpo

1.90

I .50

1.60

I .67

effort

2.50

1.80

I .I0

1.80

position

muscle

per

gaze

near the prirnary

Time

0.30

0.33

(set)

FIG. 1. Time course of isometric tension of a human lateral rectus muscle during saccadic eye movements of 15 and 30 deg of the patient’s free eye directed toward the side of the muscle (T) or away from it (Nj and back again to the primary position (0 “je The muscle was held at its primary position length.

of 0, =t 15, and &30 deg. The range of variation within the five trials at each point was about 10 %. It was about 20 % from beginning to end of any one study. There was no constant trend to indicate muscle fatigue even at the abnormally high tensions created by the isometric condition. These variations were probably due to small head movements. The passive length-tension curve of the muscle is also shown in Fig. 2 (curve PM). In order to obtain the tension of the active portion of muscle, the passive curve is subtracted from each of the total tension curves resulting in the dashed curves which relate developed tension to length. The dashed curves of Fig. 2 indicate that L,,, the length at which muscle exerts maximum developed tension occurred 6.5 mm beyond L,. Since the average rectus length at L, is about 40 mm, L, is 0.86 L, and over the eye movement range of =tr50 deg the muscles work over the range 1.07 L, to 0.65 L,. Developed resting tone in the primary position T, for this muscle was 17 g (point B in Fig. 2). The slope K, of the lengthtension curve through point B is 0.5 g/deg. If the horizontal recti muscles are similar, a gaze effort of 15 deg will cause the agonist to increase its isometric tension by 26 g (B to A in Fig. 2 and the antagonist to decrease

ROBINSON,

O’MEARA,

SCOTT,

10

Globe

rotation

(mm

20

AND

30

4G

COLLINS

T

or deg)

3. Steady-state relationship between tension applied to the human eyeball and its subsequent horizontal rotation with both horizontal recti detached. Upper right quadrant contains actual Lower left quadrant assumes symdata for temporal (T) rotation. metry for nasal (N) rotations. FIG.

Change

in muscle

length

(mm

or deg)

2. Partially innervated length-tension curves for a human extraocular lateral rectus muscle. Change of muscle length from the primary position length is given in millimeters (first row) and its equivalent value in eye rotation (second row) if the radius of the eyeball is taken as 11.6 mm. Each curve is for a constant effort equated with the actual deviation of the unoperated eye temporal (T) or nasal (N) with respect to the eye under study. Curve PM is Solid lines indicate the smoothed bethe passive muscle tension. havior of total tension. Dashed lines are developed tension obtained by subtracting curve PM. FIG.

its isometric tension by 11 g (B to C in Fig. 2 j. The net change in isometric tension per degree of effort (&j as it would be measured in the intact eye would be the sum of the force changes (37 gj divided by 15 deg or 2.5 g/deg. This constant is also shown in Table 1 for patients B and C. Passive muscle tension. The passive length-tension relationship was approximated by our asking patient A to fixate a target lamp as far as possible out of the muscle’s field of action. This should have maximally inhibited the muscle. Curve PM in Fig. 2 is the result. It is nonlinear. Tension is first developed at a length 3 mm short of Lp. The slope, Kpm, at L, is 0.2 g/deg and increases at greater lengths. This relationship was determined in this way in only one patient. To obtain additional measurements of K,, and verify that the muscle was relaxed, the passive muscle length-tension curve was obtained on five additional horizontal recti on four patients under general anesthesia. They are patients D-G in Table 1. They included one female and three males ranging in age from 2 to 44 years. The results were in close agreement with each other and with that of patient A. The value for Kprn shown in Table 1 is the mean of patients D-G. The passive muscle component was quite viscous and when lengthened rapidly by a small increment (manually by means of a wormdrive manipulator) the tension rose by about twice the

steady-state change to which it decayed with a time constant of about 4 sec. Passive globe tension. With both horizontal recti detached, the steady-state tension required to rotate the globe in its bed of suspensory tissues with the four remaining muscles attached is shown in Fig. 3. The slope of this curve at the origin, K,,, is 0.5 g/deg. This curve is also nonlinear but less so than that for passive muscle tension. The orbital tissue bed is also quite viscous. When the globe was rotated quickly (by hand as before) by a small increment, the tension rose initially to about twice the change in steady-state value and decayed with a time constant of about 8 sec. It was necessary to wait almost 15 set after each globe rotation to be sure a new steady state had been reached. Table 1 indicates the value of K,, for patients B and C. Dynamic behavior. Figure 1 also shows the dynamic behavior of isometric muscle tension as the lateral rectus played the role of agonist and antagonist in 15and 30-deg saccades at the primary position length. As an agonist it produced a burst of force whose peak change was about 52 and 64 g for the O-15 and O-30 deg movements, respectively, before decreasing to a new steady-state value. Although eye movements were not monitored, it is known that the eye, in the normal situation, would reach peak velocities of 300 and 500 degjsec, respectively, under these applied forces (lo>. The peak rate of change of isometric tension was 1,600 g/set. The ratio of peak to steady-state isometric tension was smaller for the larger movement. As an antagonist, the tension of the muscle fell almost to zero before resuming a new steady value. The duration of human saccadic eye movements is well documented (9, 15, 26) and the normal durations of 15- and 30-deg saccades are about 55 and 8,O msec, respectively. This agrees with the durations of the heightened (or inhibited) activity in Fig. 1 defined as the time from the start to the peak (or trough) of tension and indicates that for movements of this amplitude the time in which the agonist is highly activated and the antagonist inhibited is the same as the duration of the saccadic movement itself. Following this period of activity the isometric tension of the agonist fell slowly and required about 600 msec before reaching a new steady state.

MECHANICAL

COMPONENTS

OF

EYE

551

MOVEMENTS

DISCUSSION

The discussion is divided into static and dynamic behavior and a consideration of the consistency of the data with themselves and the research of others. Statics: active tension. An important finding of this study is that L, lies at a muscle length greater than L, by an amount corresponding to an angular deviation of about 32 deg. Investigators in this area (6, 7, 15, 16) have assumed for lack of evidence that L, and L, coincided. Since developed tension does not vary greatly in the vicinity of L, these investigators ignored the lengthtension relationship of the contractile components of the muscles. This is clearly not the case and, in fact, the active muscle spring constant K, is larger than the other two sources of static spring stiffness K,, and K,,. Statics: passive tension. The steady-state load which the active part of muscle must overcome in steady deviation of the globe is the passive spring stiffness of both antagonist muscles plus that of the globe suspensory tissues. If one assumes that the medial and lateral recti are mechanically similar then the passive load for a muscle pair may be constructed. Such a net curve would have (for patient A) a slope through the origin of 2 EC,, or 0.4 g/deg. This curve may then be added to that shown in Fig. 3 for the suspensory tissues to yield the total length-tension curve of all the passive tissues of the orbit involved in horizontal movement. The net slope of this curve at the origin is 0.9 g/deg for patient A and the total curve (P) is shown in Fig. 4. Summary of static forces. Figure 4 is a summary of the static forces of gaze fixation. For any angle of horizontal gaze it permits one to estimate the holding xi 100, c :L E

80

z !i

60 40

SOoN I-

l 40 Temporal

1 30

I 20

I IO

0

Eye rotation

I IO

(deg)

1 20

I 30

I 40 Nasal

4. A composite of all the static forces in eye positioning. Partially innervated developed tension-length curves (as in Fig. 2) for the lateral and medial recti are shown above and below, respectively, in dashed lines. Their sums for gaze efforts of 0, 15, and 20 deg nasally (N) and temporally (T) are in solid lines. Curve P is the combined force of passive muscle components and globe suspensory tissues. FIG.

forces in each muscle and the restraining force of all the passive orbital tissues. The dashed lines in the upper half of Fig. 4 are a reproduction of the dashed lines of Fig. 2 showing the relation of developed tension to muscle length and effort for the lateral rectus. If the medial and lateral recti have the same length-tension relationship (although the medial rectus is probably somewhat stronger) then the developed tension curves of Fig. 2 may be reproduced upside down and backwards to represent the length-tension relationship of the medial rectus. The solid curves of Fig. 4 are the sum of the medial and lateral rectus curves for each effort and represent the relationship between net developed tension and eye position. Curve P is the sum of the passive muscle tissues of both medial and lateral recti and the globe suspensory tissues as described in the previous section. This curve is plotted with a negative slope because the eye deviation produced by any gaze effort is then easily found as the intersection of P with the net active muscle curves where the two tensions, net active and net passive, are equal and opposite. If the active and passive data, which were independent measurements, are compatible, the intersection points A and B for the 15- and 30-deg temporal efforts with the load line P should occur above the points on the abscissa corresponding to 15 and 30 deg of abduction, respectively. In fact, they lie above the points 20 and 35 deg. In view of the assumptions made and the degree to which conditions could be controlled this agreement is considered good. Figure 4 indicates that over the range a40 deg the holding force required of the agonist does not exceed 45 g. Yet the muscles are capable of exerting much more force. Figure 2 shows a value as high as 110 g and the largest transient saccadic tension seen in the study was 130 g. Thus it seems clear that the size and. force capability of the extraocular muscles is not related to the task of steady eye deviation but to the large forces required to make saccadic eye movements so rapidly. It must be pointed out that the interpretation of the data on the statics of active tension depend on whether there is a stretch reflex for the extraocular muscles. There is electrornyographic evidence for (4, 13) and against such a reflex (19) in man and fairly reliable evidence against it (8, 24) in animals in which, however, stretch afferents have been clearly demonstrated. There are intermediate views (2) which hypothesize a long latency stretch reflex only to slow tonic muscle fibers that respond with graded contractions rather than by twitches and action potentials. Although the evidence against a short latency monosynaptic reflex is good the possibility of a slow reflex involved perhaps in maintaining tone cannot yet be rejected on experimental grounds. If such a reflex exists the changes of developed tension accompanying changes in muscle length arise from two sources, mechanically from the length-tension relationship of muscle (independent of a nerve supply) and neurogenically from the stretch reflex. Thus a portion of the mean value 0.43 g/deg

552 and the lines in for K, (Table 1) may be neurogenic, Fig. 2 for a constant gaze angle of the contralateral eye may not be lines of constant innervation because the latter would then depend on both the gaze effort by the patient and the muscle length. This does not affect the measured data or the curves in Fig. 4 since the force of a muscle is still uniquely determined by its length and the effort associated with the gaze deviation of the opposite eye whether or not there is a stretch reflex. If a stretch reflex does exist then effort may not be equated with innervation and the length L, is a functional L,, that is, the length at which the nervemuscle combination (with a stretch reflex) achieves tension rather than that length ma .ximum de veloped at which the denerva .ted muscle alone might develop maximum tension. Dynamic behavior. It has already been established that saccades are produced by a large burst of activity in the agonist and complete inhibition in the antagonist. The evidence comes from electromyography (3, 14, 20) and from single-unit recording in the abducens nuclei (18) and its cranial nerve (25). The mechanical correlate of this pulsatile activity is demonstrable in the net isometric muscle tension in the immobilized intact eye (15). The pulsatile nature of the activity of the extraocular muscles during saccadic movements and the fact that the pulse duration is the same as the saccade duration is well supported by the records of Fig. 1. They show, for the first time, the time course of isometric tension during a saccade of an individual muscle. At the end of the saccade or pulse of active-state tension the isometric tension in the agonist does not fall at once to its new holding level but decays to it rather slowly. We feel that the explanation of this lies in the viscoelasticity of the passive elements which stress relieved, as described, with time constants of 4-8 sec. If the active muscle force fell to its holding value at the end of a saccade, the passive viscoelastic elements, which were abruptly stretched by the saccade, would stress relieve as time went by and cause the eye to drift beyond its desired goal. To prevent this, the extraocular muscles decrease their force gradually (perhaps in a preprogrammed manner) to just counterbalance the stress relaxation of passive tissues and maintain the globe in its position. This behavior reinforces the idea that viscosity constitutes a major source of impedance in eye movements. The records in Fig. 1 reflect the corruption of the time course of muscle active-state tension by the seriescomponent and force -velocity rela tionsh ip of elastic the con .tractile component. A knowledge of these components is desirable for understanding the dynamics of eye movements. Of special interest is the force-velocity a source of viscous relationship since it constitutes damping. It has been established (5, 15) that, except for a small underdamped subsystem (17,Z l), the mechanical elements of the orbit are heavily overdamped. This viscous damping is the greatest impedance to rapid eye movements and is what necessitates the pulse of extra force for saccades. In a theoretical study, Cook

ROBINSON,

O’MEARA,

SCOTT,

AND

COLLINS

and Stark (6, 7) suggested that most of this viscosity is in the force-velocity rel ationship of the muscles. Unfor tuna tely an attempt to evalua te these components from the records of Fig. 1 is beset with many difficulties. The exact time course of active-state tension for agonist or antagonist is not known. It is not known to what extent the three types of muscle fibers, fast twitch, slow twitch, and tonic (l), participate in total muscle tension The mechanical properties, especially the force-velocity relationship, of the fiber types is unknown. The fraction of active fibers before and during the pulse of activity or inhibition is unknown and this determines the net effective series-elastic and contractile components of each muscle. The properties of the forcevelocity relationship are only known for tetanized muscle. How partial innervation at discharge rates well below fusion affects the force-velocity relationship is unknown. The behavior of the force-velocity relationship during simultaneous relaxation and lengthening has never been studied. The relaxation phase for shortening muscle has been studied by Jewel and Wilkie (11) and lengthening muscle by Katz (12) but they concerned frog muscle at 0 C and the extrapolation to human extraocular muscle at 37 C is questionable. The study of Katz raises the question of slipping of mechanical linkages in lengthening muscle. It is unlikely that the tonic fibers in the antagonist can relax quickly enough during a saccade and it may be necessary to hypothesize that they slip, which greatly obscures the relation between tension and lengthening velocity. These considerations make it unprofitable to speculate on the interpretation of the isometric tension records of Fig. 1 until more is known about the dynamic mechanical properties of muscles under the conditions that exist when they work in the body. Consistency of data. One source of error was the difliculty in determining L, exactly. This was estimated by eye by the surgeon and is thought to have been correct to within rfi 1 mm. This type of error has the effect of translating the curves in Fig. 2 to the left or right. Errors due to head movement have already been mentioned. Despite these sources of error we feel that the self-consistency of the data was good within each experiment considering the degree to which conditions could be controlled (e.g., points A and B, Fig. 4) Interpatient differences (Table 1) are difficult to interpret and may represent true individual differences, sex differences, or may reflect abnormalities of muscle innervation since patients A , B, and C had in termit tent exotropia preoperatively. These vari .a tions point UP principally the small sample size and the need for further observations. The mean values in Table 1 are simply presented as the best presently available. Robinson ( 16) measured the net static spring constant of the intact eyes of three subjects and Childress and Jones (5) of one subject. This constant is 1.2 g/deg and showed little interperson variation. The data reported here may be compared to this number in two ways. Small displacements of the intact eye from L, should

MECHANICAL

COMPONENTS

OF

EYE

553

MOVEMENTS

create force changes due to K, and KPnz of each muscle and KPO. The total spring constant K, should be the sum of Z(K, + Kpm) and K,,. The mean value shown in Table 1 is 1.67 g/deg or 39 % above the previously reported value of 1.2 g/deg. Since Kpm was not measured for patients B and C the mean value for patients D-G was used to calculate K,. It is easy to show that if one measures the net change in isometric muscle tension for each degree of gaze effort from the primary position the spring constant obtained (KJ should equal K,. Table 1 indicates considerable spread in K, and a mean value of 1.8 g/deg which is 12.5 70 above the mean value for K, and 50 % in excess of the value of 1.2 g/deg. Although our calculated values for the net spring constant are somewhat high we nevertheless feel that considering the small sample size and the difficult conditions under

We thank Dr. A. Jampolsky without whose enthusiasm, encouragement, and participation these studies would not have been performed. We are greatly indebted to Dr. Frank Hull of the medical facility at Vacaville, Calif. for his kind cooperation. We also thank Mr. Frank Evans for technical assistance. These investigations were supported by Public Health Service Research Grant AM-05524 from the National Institute of Arthritis and Metabolic Diseases, Public Health Service Program Project Grant NB-06038 from the National Institute of Neurological Diseases and Blindness, and Grant NONR-3009(00) from the Office of Naval Research. Much useful equipment and helpful services were provided by Public Health Service General Research Support Grant 5 SOL FR-05566. Received

for

publication

30 July

1968.

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25.

26.

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